Hi, I try to solve for finding equity when 5bet bluff but I am not very good with prorities in operations.

In my example MP open 5$, SB 3bet 20$, BB fold, MP 4bet to 48$, SB would shove (180$ more). We know that MP will only call 6 combos out 35.7 combos. so he calls 6/35.7, or 16.81%.

So I calculate like this :

0 = 70(0,8319) + (0.1681)(402X - 180)

Then I don't understand how to isolate the X.

I tried like this :

0 = 58,23 + 67.5762X - 30.258 (I guess my mistake is somewhere there)

then -27.972/67.5762 = X

I tend to ignore the - sign, and come up with 41.39% but the thing is it then does not add up. I know it's not the right number.

Anyone have an idea ? Thank you!

Do both villain's cover the 180 raise? If so then they both started with 228 and the total final pot should be 456 not 402. It doesn't change the calculation though.

So the way I would approach this question is notice that the only way this equation can ever be negative is if

(0.1681)*(402*X-180) < -70*(0.8319)

Less than meaning a more negative number.

So if we multiply everything out:

67.5762*X - 30.258 < -58.233

So now here is the question, is it possible to add a positive numer to -30.258 to reach -58.233? The answer should be no.

Now let's go back to our original equation we can test this out. Let us assume you have 0 equity when called. We'll remove the equals 0 for now:

70(0,8319) + (0.1681)(-180)


58.233 - 30.258 = 27.975

So you don't need ANY equity for this play to be profitable and setting the equation equal to 0 makes no sense.

Now let's assume you know that calling instead of jamming has an EV greater than 27.975. At that point you could determine how much equity you would need to make jamming better than calling.

Hi Just Grinding,

Sorry it's a 1-2$ blinds cash game and we are both 100bb deep, so 200$ stacks. MP open 5$, SB 3bet 20$, BB folds, MP 4bet 48$, so the 5bet is 200$, the raise is 152$ more, but what I meant is the cost of the bluff is 180$ more. Yes both villains cover.

Thanks for the reply.

No problem. I figured as 100bb structure is pretty standard which is why I asked.

No problem feel free to respond with anything.

Also anytime you get a negative number when you shouldn't (i.e. negative EV is ok but negative probabilities is not) or you get a calling equity greater than or 50% you know something when wrong :-)

5Bet/(Pot+5Bet)=Equity needed, that is:

$180/($20+$48+$2+$180)=72%

The SB needs to win 72% of the time to break even.
MP must defend at least 28% to not let the SB auto profit. You explained how MP is only calling 17% of the time.

Therefore SB can 5bet jam 100% of hands (you need to include rake in the calculations if the decision is close; this decision is not).